About bully, I don't think kid at 4-5 years old that really understand it. And the teacher here, usually has zero tolerant for bully.
eg. My daughter is a kid that usually bullied other kids in class in the view of the teacher. So we got warning notes in communication book, and sometimes even phone message, when talking with her, she doesn't think she bullied other kids, she thought it was for fun and play with them.
When you thought teacher didn't take action, the teacher could already notify the other side's parents.
for us, we taught her if the other kid said "stop", just stop it, because he/she didn't like the way you played.
For clothing, my kids don't care at all. she normally wear the same snow suits for 2 years.
and she only has one pair of mitten in the winter, I usually dried them at night, so she can wear them again tomorrow.